In an interview Thursday, Mr. Schumer said he and Ms. Pelosi arrived at Wednesday’s dinner prepared with a specific list of border security items that Democrats could agree to, drawn from Mr. Trump’s own budget request. They included sensors to beef up border monitoring, rebuilding roads along the border, drones and air support for border enforcement.

“I told the president that there’s tremendous distrust in our caucuses, in our constituencies and in the public, and I mentioned a litany of things such as the Muslim ban and Charlottesville,” Mr. Schumer said, referring to the president’s travel ban on immigrants from six Muslim-majority nations, and to Mr. Trump’s equivocal remarks about white supremacists after the violence in Charlottesville, Va.